Comparing and Ordering Numbers

Why we compare and order numbers

Every day we ask which is more and which is less. Who scored the higher mark? Which item is cheaper? Which class has the most children? To answer these questions clearly, we compare numbers (decide which is bigger or smaller) and order them (line them up from smallest to largest, or the other way round). This lesson gives you a reliable method that works for numbers of any size, from two-digit numbers to thousands and beyond.

The secret behind all of it is place value — the idea that a digit's worth depends on its position. If you would like a refresher first, our lesson on place value with tens and ones explains the foundations.

The three comparison symbols

There are three symbols we use to compare two numbers:

Symbol	Meaning	Example	Read as
>	greater than	8 > 3	"8 is greater than 3"
<	less than	3 < 8	"3 is less than 8"
=	equal to	5 = 5	"5 is equal to 5"

Here is a trick to never mix up > and <: the symbol is like a hungry mouth, and it always wants to eat the bigger number. The wide open side faces the larger number; the small pointy side faces the smaller one. So in 8 > 3, the open mouth faces the 8. In 3 < 8, it still faces the 8. The mouth is always greedy for the bigger amount. You can explore these symbols further in more than, less than and equal.

How to compare numbers step by step

Follow this method and you will never go wrong:

1. Count the digits. If one number has more digits than the other (and there are no leading zeros), it is the larger number. For example, 1,250 (four digits) is bigger than 999 (three digits).
2. If the digit counts match, compare from the left. Start at the largest place value — thousands, then hundreds, then tens, then ones. Compare one place at a time.
3. Stop at the first place where the digits differ. Whichever number has the bigger digit there is the bigger number. The places after that no longer matter.

This works because the leftmost digit carries the most value. A bigger thousands digit beats any combination of smaller digits to its right.

Worked example 1: comparing two-digit numbers

Compare 47 and 74.

Both have two digits, so look at the tens place first. 47 has 4 tens; 74 has 7 tens. Since 7 tens is more than 4 tens, 74 is the larger number. We write:

47 < 74 (47 is less than 74).

We did not even need to look at the ones digit, because the tens already decided it.

Worked example 2: comparing when one number is longer

Compare 89 and 205.

Count the digits: 89 has two, 205 has three. More digits means a bigger number (these have no leading zeros), so:

89 < 205.

Here the digit count alone gives the answer — the actual digits 8 and 9 do not matter, because 205 reaches into the hundreds and 89 does not.

Worked example 3: comparing larger numbers digit by digit

Compare 6,200 and 6,020.

Both have four digits, so compare from the left:

• Thousands: 6 and 6 — equal, keep going.
• Hundreds: 2 and 0 — different! 2 is bigger than 0.

We can stop here. Because the hundreds digit of 6,200 is larger, 6,200 is the bigger number:

6,200 > 6,020.

Notice how comparing from the left saved time — we found the answer at the hundreds place and never needed the tens or ones.

Putting numbers in order

Once you can compare two numbers, you can order a whole list. There are two directions:

• Ascending order — smallest to largest (climbing up).
• Descending order — largest to smallest (coming down). A handy hint: descend sounds like down.

To order a list, compare numbers in pairs and slot them into place, smallest first (for ascending). It helps to first group numbers by how many digits they have.

Worked example 4: ordering a mixed list

Put these in ascending order: 305, 35, 350, 3,005.

First, sort by digit count:

• 35 has 2 digits — the smallest group.
• 305 and 350 have 3 digits.
• 3,005 has 4 digits — the largest.

Now order within the 3-digit pair: 305 and 350 share the hundreds digit (3), so compare tens: 0 vs 5. So 305 < 350.

Putting it all together, ascending order is:

35, 305, 350, 3,005.

To get descending order, simply reverse it: 3,005, 350, 305, 35.

Watch out for tricky traps

• More digits does not always mean bigger if there are leading zeros. Normally we do not write numbers with leading zeros, so 042 is just 42.
• A longer-looking number is not automatically bigger if you misread it. Always line up the place values carefully.
• Equal numbers exist. If every digit matches, the numbers are equal, and you use the = sign.

Why this matters

Comparing and ordering are everywhere in real life and in maths. You compare prices when shopping, compare scores in games, and compare measurements in science. In maths, ordering numbers is essential for reading charts, finding the largest or smallest value in data, and rounding sensibly. The place-value method you learned here also powers bigger skills later, like ordering decimals and negative numbers. Once you trust the method — count digits, then compare from the left — you can compare any numbers with confidence.

Try it yourself

1. Symbol practice. Write five pairs of numbers and place the correct symbol (>, < or =) between them. Remember: the open mouth faces the bigger number.
2. Digit-count race. Mix up cards showing numbers of different lengths (like 7, 84, 102, 2,310). Sort them fastest to slowest by counting digits first.
3. Order the team. Write the scores of six players on slips of paper. Put them in ascending order, then flip to descending order. Who came top? Who came last?
4. Real-world compare. Find two prices in a shop or two distances on a map. Which is greater? Write it using the correct symbol.

Practise the "count digits, then compare from the left" method until it feels automatic — it is the key to comparing any numbers, however large.